Reorder u8 values for sparseobservable terms so that it is easier to determine diagonal vs off-diagonal element

[nonhermitian]

What should we add?

It would be nice if the unsigned char values for the operators in a sparseobservable were renumbered so that lower indices corresponded to diagonal operators and the higher ones off-diagonal. Then checking if the operator is diagonal for a given qubit is a simple operator_u8 < num_diag_terms check.

[jakelishman]

The exact numbers are part of the stable API in order to enable interaction with Numpy and can't be changed without an API break. If you hadn't seen it, the logic behind the choices of numbers is described here: https://docs.quantum.ibm.com/api/qiskit/dev/qiskit.quantum_info.SparseObservable#bitterm.

The is_diagonal check is something like (term & 0b11).bit_count() % 2 == 0, which can be Numpy-vectorised, if that's useful for you? edit: sorry, that's not right - one sec

[jakelishman]

It's term & 0b11 == BitTerm.Z. Got there in the end.

(edit: or not (term & BitTerm.X), I suppose)

[jakelishman]

If it's helpful, we can add a function BitTerm.is_diagonal as a feature that can be used either as an instance method or as a standalone function that will do it in a Numpy-vectorised way, so you can do BitTerm.is_diagonal(arr) or my_term.is_diagonal()?

[nonhermitian]

If it is stuck the way it is then no worries. In practice knowing the number of, and location of off-diagonal terms is quite important. I have gone down the road of numbering diag lower than off-diagonal, but a helper function likely works just as well I think.